Cascade machine



Dec. 1, 1925.

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F. CREEDY CASCADE MACHINE Filed July 30, 1921 9 Sheets-Sheet 9 5&5 5 bbbbw E awwwwawwwaww QQQQQQQQQQQQQQQQQQQQQQQ W WWwwwfiwwmiw Patented i,

FREDERICK 'OREEDY, F ILKLEY, ENGLAND.

CASCADE MACHINE.

Application filed July 30, 1921, Serial No. 488,686.

To all whom it ma concern Be it known that I, Fnnnizniou Cnuror, a subject oi the King of Great Britain and lrelanchand a resident of lishburn Place,

5 Ilklcy, Yorkshire, England, have invented certain neiv and useful Improvements in Cascade Machines on which application has been made for Letters Patent in Great Brit ain, No. 23123, filed on 5th August, 1920; and No. 36540, filed th December, 1920), of which the following is a specification.

The present invention relates to alternating current ascade machines.

lVith a pair of induction motors coupled in cascade in the known manner with the rotor windings of one connected to the stator windings of the second, the rotor windings of the second are connected through resistances. At starting these resistances are gradually out out whereby the motor comes up to its cascade speed. The rotor windings of the first machine may also be connected through resistances the gradual cutting out of which causes the speed to rise until when they are short circuited, the second motor is cut out and the machine runs at a speed corresponding to the pole number of the field produced by the stator winding of the first machine.

The advanta es of operating alternating current motors in cascade have led to the derelopment of a type (it machine equipped with two windings upon both stator and rotor, interconnected and controlled in the same manner as the windings of two separate cascade-connected motors. From this in turn acertain number of designs have been arrived at in which a single winding on each part reoroduces the effect of the two windings which it replaces The present invention relates to machines (it this latter liillCl, herein referred to as internal cascade machines. Its lirst and main purpose is vastly to increase the range of usefulness of such machines. Subsidiary aims contrilnlting to this end are to enable windings, and therefore machines, to be constructed for pairs of pole numbers of other ratios than 2:13 to facilitate and improve the design of internal cascade windings; to provide secondary internal cascade windings capable of operating upon more than one pair of poles to provide primary windings to cooperate with such secondary windings by producing a field of any one of a plurality oi? different pole millili ers; (did by acting as a secondary on any one of a pinrality, of pole numbers; to provide improved means for causing an internal cascade machine to rise to and run at a speed correspond ing to one of its basal pole numbers, herein termed a basal speed, and thereby to enable the construction of machines of many and wide ranges of speed variation; and also iurther to increase the flexibility of a machine by providing awinding capable of acting as a secondary and simultaneously or alternatively as a primary.

lVith these purposes in view my invention comprises in one aspect thereof, an internal chine, having such a Winding as just mentioned upon one member, and suitable primary windings upon the other member; and my invention includes primary windings for this purpose, adapted also. to act as secondary windings upon a second pole number. In such a machine my invention provides improved means for hindering rotation of the primary field with respect to the rotor, and thereby causing the rotor to attain a basal speed. In its fullest development my invention contemplates an internal cascade motor having secondary windings adapted to operate on more than one pair of pole numbers, and primary windings adapted to produce various primary fields and to act 'as secondaries in other fields, together with means for changing the primary pole number, and for resistance control of the secondary, whereby the machine may be brought without shock from one to another of a wide range of speeds.

In the accon'ipanying drawings Figure 1 is a diagran'i explaining the ideal distribution of ampere conductors in a single rotor winding acting as a secondary on one pole number and as a primary on another:

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Figure 2 is a diagram of a specific cascade winding;

Figure 3 shows the phases of currents in it on a ditierent pole number;

Figure 4 shows the winding modified to enable the motor to attain another than the cascade speed;

Figures 5 and 6 show the distribution of ampere-conductors in this winding;

Figure 7 shows a further modification oil the winding for enabling the motor to attain another than cascade speed;

Figure 8 is another form of the diagram of Figure 2;

Figures 9 to 13 are other specific rotor windings illustrated by diagrams of the form of Figure 2 or Figure 8;

Figures 14: to 17 represent stator windings adapted to co-operate with the rotor windings described.

Figure 18 shows the stator and rotor windings of an internal cascade machine according to the invention.

In a single or internal cascade machine having a single winding on each member the winding on one member, i. e., the stator or the rotor, acts as a primary to produce a field of one pole number (this will be called a field of P pole pairs) and as a secondary in a field of another pole number (this will be called a field of Q pole pairs), this latter field being produced by the winding on the other member. Thus this latter winding acts as a secondary in a field of the said one pole number (P pole pairs) and as a primary to produce the field of the said other pole number (Q pole pairs).

I-Ieretofore it has not been possible to build internal cascade machines to operate on fields in which. the ratio of P to Q is other than 2 to 1.

I have now discovered how windings "for such machines may be constructed to operate on fields in which the ratio of P to Q may be any value.

Two distinct types of internal cascade machines may be distinguished according to whether the two fields inter-linking the wind ings on one member, for example, the stator, revolve in opposite directions with respect to the other member, for example, the rotor, or whether they revolve in the same direction. The former type is known as the normal or cumulatively cascaded motor and the latter as the differentially cascaded motor.

My invention partly consists in a single winding for the secondary member, i. e., the winding not connected to the supply, in which the number of ampere conductors per slot is not constant as in the ordinary types of armature winding, but presents a number of maxima and minima equal to P plus Q for a normal or cumulatively cascade motor arranged. for P and Q, pole pairs,

and P-Q "for a diiferentially cascaded motor. Referring for the moment only, to the normal type of motor the winding will usually be made up 0;? P plus Q circuits symmetrically distributed round the circumference and carrying symmetrical polyphase currents of P plus Q GCM of P and ing is arranged, can be dealt with by threephase internal cascade windings, such as have already been devised, but three-phase windings will not serve for any other ratio of pole numbers for fields rotating in op" posite directions.

I have discovered that pairs of pole num bers in the ratio of 3 to 2 can be used if,

the winding is designed for five phases. Pairs of pole numbers in the ratio of 4: to 3 necessitate seven phases, and so on. But five phases is also an appropriate number for pole numbers in the ratio of 42 to 1 and seven phases is also the appropriate number for the ratio of pole numbers 5 to 2 and 6 to 1 and so with the higher number of phases.

Reference will now be made to Figure 2 of the drawings which shows a secondary winding in accordance with the present invention suitable for 4-. and 6 poles. It is spread over 20 slots numbered in the figure; the coils have a slot pitch of 14;. The winding is built up of 5 elements connected. in mesh (each element consisting of two sec-- tions connected in series reversed), together with 5 elements (each consisting oi a sing e section), joined in star and to the junctions of the 5 mesh-connected elements. .Eacb section consists of an upper conductor in one slot joined to a lower conductor in another slot (or of a number of such coils in series). This structure of the winding will be more readily understood from Figure 8, which is another diagrammatic representation of the same winding; a section shown in Figure 8 as a black circle joined to an open circle, corresponds with a section of Figure 2. The sections of Figure 8 are numbered with the. number of the slot of Figure 2 which conlill) esa rm tains the upper conductor of the section. It will be seen that the even numbered sections are all in mesh, and the odd numbered. in star, the upper conductor of an odd section being joined to the junction of the lower conductors of the even sections on each side of it. It .is obvious from Figure 8 that the winding presents five symmetrical closed circuits, each star section being common to two circuits.

The phase ditierence between corresponding bars of these circuits when the winding is used in a l pole field, will he 360 No. of pole pairs 2 360 The phases of the currents in the respective conductors may, tl'ierefore, be marked on Figure 2 as follows. Any live evenly spaced conductors, say the up oer conductors o1 slots 4, 8, 12, 16, 2-0 may be marked 0, l lt 288, 72, 216; the connect-ions of the winding then show that the phase of the lower bar of slot 5 must he 0, that of the upper bar of slot 2 and the lower bar of slot 7 must be 180, and similarly determines the phase of all the n'iesh-connected conductors; the phase ot' the lower bar of slot 8 must be intel-mediate between the phases of tlie lower bars of slots '1' and 9, which determines it to he 162, and determines the phase of the upperconductor oi slot 5 as 3&2"; and so on for the ren'iaining star-connected bars. The coils have aslot pitch of l to 4, i. e. a. normal pitch which is understood to be a pitch of from slot- 1 to slot I'ht-l-l, where n is the number of slots per section. In the ligi'urc 11:1.

Figure 3 shows a secondary winding suitable for and El poles, thus the winding besuitable for l and. l pole pairs it gives 5 ruarzima oi ampere conductors and therefore is similar to the winding described with reference to Figure :2, which is suitable for pole pairs. The winding: in Fig". 3

5: and b is ronnected exactly as the winding in Fig. :2, the phase diil'm'euce oi? the currents in corresponding:conductors being diilj erent. The phase ditiercnce between the circuits when the winding used in a 2 pole field is From whic as has been (ltf-"lil)9(l with reterence to the .iascs oi: the currents in the r ectire comluchn's may be lllttliiQCl on the lig'urc. This has been done. It will be understood that the connections of the windhave. however, been omitted for the salte clearness.

The winding has a symmetrical circuits and arranged exactly in the term illustrated in 8. the said circuits being equally spaced round the circuinten ence and carrying 5 phase currents.

The phase dillerence between the circuits in the 8 pole lield is similarly 288, but since the 8 pole field revolves in the opposite direction to the 2 pole field, the phase ditierence must be considered as 360288, which is '1' 2. Hence the same result is obtained whichever field is considered.

This illustrates a fundamental principle or he invention, namely, that the relation between the number of concentrations of ampere conductors round the perioher or" the machine and the pole pairs P and Q, must be such that the phase diiierei'ice between the E. ii. F.s in corresponding bars oi adjacent circuits on the one pole number for example P, measured in a clockwise direction, is the same as the phase difference between the E. M. FPS in the same bars on the other pole number, namely (a), when measured in a counter-clockwise direction.

The windings illustrated in Figs. 2 and 3 are typical of a large class of windings. For example, a winding for 2 and 6 poles requires i phases and may be wound in 16 slots so that it may be represented (since it gives magnetic balance without duplication) by of the diagram oi? Fig. 3.

9 is another diagrammatic representation oil such a. winding for 2 and (3 poles,

this diagram showing the arrangement 01 the circuits in a manner similar to that in which Fig. 8 illustrates the 5 circuits of the winding; described with reference to Fig. 2. It will be understood that in 9 a section consisting oi an upper conductor in one slot joined to a lower conductor in another slot or a number of such coils in series) is represented as a bl ck. circle joii ed to an open circle, as in l i 8, and this arrangement is employed throughout the present ipeciiication. v

Fig. i also shows a secondary winding of the type illustrated in 2 and but with a'rangg'ements to enable the speed of the machine to rise from the cascade speed to a speed corresponding to one of its basal or primary pole numbers. The numbers indicate the phas s oi the currents in'the conductors whei the winding is used in a tour pole field, and at its al speed.

A portion of the iiindinu i s shown in dotted lines is wound into the slots shown empty in Figures 2 and $3. This portion of. the winding is connected to slip ring? 5-, S 57:", S A. switch l. having an operating hand e (l may be operated to connect the slip rings S to and thus short circuit the portion of the winding Vi when the fluxes are hindered from rotating with respect to the secondary member on which the windings are carried and the machine runs at a speed corresponding to the primary or basal pole number.

The cascade winding is also connected at the mid points of the mesh to slip rings V V V, V", V which may he connected together by means of a switch T having an operating handle U whereby the cascade winding is arranged in a number of closed circuits which is no longer equal to or a submultiple of the sum of the two nun'ibers of pole pairs P and Thus when the switches T and T are operated to connect the slip rings S to together and the slip rings V to V together the machine will run at its hasal speed.

lVith this winding all the slots on the member carrying the winding are filled.

Figure 7 shows the winding of igure 4 with each phase or": the cascade winding arranged to be short circuited through one section of the portion TV by means of the switch T which is employed to connect the slip rings V V V V, V to which the upper bars of the portion .V are connected. When the switch T is closed the effect is the same as is described with reference to Figure 4: whereby the machine will run at its basal speed.

Figure 10 shows a cascade or secondary winding for 4; and 6 poles and having a number of open circuited sections W with means to close the circuits of said sections for the purpose of enabling the machine to run at its basal speed but without means for connecting the cascade winding in a number of closed circuits. The numbers indicate the phases of the currents in the conductors when the winding is used in a 4i pole field. The portion of the winding W which is shown in dotted lines, fills the slots not filled by the remainder of the winding which is shown in full lines. The latter part consists of 10 sections each composed of two coils in series reversed, one end of each or the sections being joined to a common star point S, while the other ends are joined alternately to one of two terminals T T F or cascade operation the terminals T T and S are permanently short-circuited. The sections of the portion VJ are joined at one end to a con'n'non star point .97) and at the other end to five slip rings S S S S S. T is a switch having an operz-iting handle U by n'leans of which the slip rings may be connected together and the portion of the winding 1V short-ci.rcuited and the machine he caused to run at its hasal speed.

Figure 11 shows cascade or secondary windingarranged similarly to that of Fig ure 7. The numbers indicate the phases of the currents in the conductors when the winding is used in a G pole field; below are represented. the conductors with the phases oi? the currents when the winding is used in a 4i; pole field. The winding is built up oi. 5 (BlQ IGl'IlIS connected in mesh, each, element cons 'ng of two sectiors connected in series reversed. and each sectioncomprising two coils, The winding is shown as having both are terminals of every element joined to a conr inon star point The mid points of all elements are brought out to slip rings S S and the star point to a slip ring S and when all of these are short-circuited together by means of the switch T the machine runs at its basal speed.

Figure 12 is a diagrammatic representation in the manner of Figure 8 of the winding of Figure 11.

The angles of the lines representing sec tions of winding in Figures 8, 9 and 12 indicate the relative phases of the currents in the sections.

Fig. 13 shows another star-mesh cascade winding of the same general type as Fig. 8 arranged for and 7 pole pairs. It is of 2% sections which are numbered in order around the circumference of the machine and which fall into two separate groups and Y. The phases of the E. M. F.s in the several sections of the Winding when operating in a field of ll poles rotating counter-clockwise and when operating in a field of 10 poles rotating clockwise are shown in the following table 2- l Group to 1 Phase in Phase in Phase m Number of section 10-p01e which 14-po1c Iii-pole field section fi 81d field belongs reversed 0 X 0 O 75 Y 105 255 150 X 210 150 225 Y 315 300 X 300 165 Y 15 315 240 X 120 .240 315 Y 225 135 30 X 330 30 105 Y 285 180 X 180 180 255 Y 285 75 330 X 30 330 45 Y 135 225 120 X 240 120 19.3 Y 345 15 270 X 270 345 Y 195 165 60 X 300 ()0 From a comparison of the second and last columns of the table it is apparent that the phases in the sections oi groups Y are oppo site when the winding operates in the two fields respectively. From this it is clear that a portion oi the winding X operates on 10 or i l poles, since the phases of the E. M. F.s in the sections are the same on both these polo nun'ihers; the phases of the M. F.s in the group Y are opposed on the 10 and 1d pole fields, which means that in the conductors in each slot occupied by this group opposite E. M. F.s are induced by the two fields so that the group Y of the winding is. for cascade operation, not re qnired. Thus. the terminals AAA of the group X. are short-circuited as indicated in 17 by dotted. lines B 13 B and the lOO CID

terminals of the winding Y are connected to slip rings 3, S, S.

T is a switch by which the slip rings may e short-circuited. For cascade operation the switch T is open and to cause the machine to rise to its basal speed the switch '1 is closed to short-circuit the slip rings and thus mnect the terminals of the group Y.

it has been pointed out that the characteristics of a winding for a given pair of pole numbers are also the requisite characteristics tor certain other pole numbers. I have discovered that a winding adapted for a given cascade speed may, if suitably designed, operate on any pair of pole numbers, the sum oi? which corresponds to that speed. Oon sequently if primary windings are provided capable of producing one pole number, and acting as a secondary to the other pole number on each of two or more pairs of pole numbers giving "the cascade speed for which the secondary winding is designed, the motor will run satisfactorily at the cascade speed, whichever of its pole numbers the primary windings are producing; and the prin'iary windings may be changed from the one pole number to the other without affecting the running of the motor. Changing the pole number will merely change the order in which the phases occur in the secondary; for instance, a setof five phases is capable of two distinct orders, viz, 0, 72, 144. 216, 288 and 0, 1%", 288, 72, 216; the first order corresponds to, say, 2 and 8 pole pairs, and the second to 4 and 6 pole pairs; in general a phases are capable of possible orders. secondary member has short-circuiting means for producing addltional circuits as described, for example, with reference to Figures a or 7 it may be caused to pass from the cascade speed to the higher basal speed corresponding to any of the pole numbers the primary winding can produce, by first causing the primary winding to produce the desired pole number, and then closing the short-circuiting means of the secondary. Thus, if the secondary winding is a 5 phase winding, adapted for a cascade speed corresponding to 20 poles, and the primary winding is capable of being modified to produce i, 8, 12 or 16 poles while acting as a secondary on 16, 12. 8 and 4. poles respectively, the motor will not only run on the 20 pole speed with each modification of the primary winding, but can be raised to a basal speed. corresponding to any one of these pole numbers by first modifying the primary winding to produce that pole number and then closing the short-circuiting means of the secondary. As a rule a ma.- chine operating on the comparatively low It follows that if the speeds corresponding to 8, 12, 16 and 20 poles will not be required to operate on 4i poles.

For simple cascade working it is easy to provide two distinct windings on the stator. For in any set off evenly spaced sections a balanced system of polyphase E. M. Fs will begenerated by a field of any number of pole pairs which is not equal to or a multiple of the number of sections; so that if 1011 a set of sections are joined in series the resultant E. M, F. in them will be zero. Hence star-connected windings devoid of parallel circuits, designed for any two pole numbers which are not multiples the one of the other, will be mutually non-inductive. But there is a great advantage in employing a single stator winding, particularly where the machine works on more than one pair of pole numbers; and it is possible to do so in 1.1121113 CEISGS'.

Some typical stator windings are next described suitable to co-operate with rotor windings such as have been described above.

Figures 1st and 15 show a Winding of 24: sections adapted to act as a primary 011 16 poles and as a secondary on 4: poles, as a primary on 4 poles and as a secondary on 16 poles, as a primary on 12 poles and as a secondary on 8 poles, and as a primary on 8 poles and a secondary on 12 poles. The principles of its construction, however. are

applicable to any pair of pole numbers which divided by their G. G. M. give the one an even and the other an odd quotient.

The winding is built up of units each of which includes four sections evenly spaced around the periphery of the stator and represented by a line joininga black circle to anopen circle, as for example, sections 1, 7, 13, 19. Each section consists of one or more coils in series. Now on 4 and 12 poles, sections 1 and 7 will be in opposition of phase, and so will, sections 13 and 19; on 8 and 16 poles all four sections will be in phase. Section 19 is joined in series with section 1, and section 13 in series with scction 7; the pairs 19, 1 and 13, 7 are then joined in parallel to form a closed circuit in which the beginning of section 19: is connected to the beginning of section 13. and the end of section 1 to the end of section 7 Terminals e, f, g, h, are connected to the junctions ofthe sections. If terminals 6, are connected to a source of supply and terminals f, it are joined through a resistance the primary currentswill be such as are required for 8 and 16 poles, while; secondary currents such as would be induced by a 4 or 12 pole field can flow through terminals f, 7iand the resistances. If conversely terminals 1,71 are joined to a source of supply and terminals 6, are joined through a resistance, the primary currents will correspond with at or 12 poles, and an or 16 pole field lot) can induce secondary currents through the resistance.

There are six such units in the winding which may be numbered 1 to 6, each taking the number of the lowest numbered section in it. For 16 poles they are joined in a three-sided mesh, the sides being formed by pairs of units in series, viz: 1 and 4c, 2 and 5, 3 and 6; the angles of this mesh may be joined to a three phase supply L L L through the switch SYV by putting it over to its left hand position. It, instead, the switch is put to the right, the angles of the mesh are short-circuited and the mid-points of its sides are joined to the supply; units 1 and at are then in parallel and form one arm of a star, and so with units 2 and 5, and and 6. So connected the winding gives 8 poles.

Figure also shows a stator winding of 2 1 sections built up of units each of which includes four sections evenly spaced around the periphery of the stator in the manner of the winding illustrated in Fig. 1 1. Relerring to the units by the lowestnumbered section in each, units 2, 1 and 6 are in series between one pole L of the source and the mid-point of the winding of an auto-trans former connected to tern'iinals L L of the supply; units 1, 3 and 5 are also in series and tapped across a part of the transformer winding giving 0.866 of the line voltage. This winding acts as a primary on 12 poles and as a secondary on 8 poles.

Figure 16 shows a stator winding for 2 and 6 poles, that is, in which the numbers of pole pairs are both odd. This winding may be employed with a rotor winding of the kind illustrated in Fig. 9 for a motor capable of running at the cascade speed corresponding to 8 poles and at basal speeds corresponding to 2 and 6 poles respectively.

The win-ding has 5st sections and is built up of units each comprising two oppositely connected sections, as for example, 1 and 28; three such units are connected in series, and three such sets of three units are connected in parallel, corresponding sections of the three parallels, for example, 18, 36 and 5 1 being evenly spaced round the stator.

l ariable resistances z are connected be tween the junctions C C C of the first and second units in the three parallels and other resistances Z between the junctions D D D of the second and third units. Three sets of three parallels are connected at one end to a common star point and at the other end to the terminals of a three-phase supply.

The directions of the lines representing the sections represent the relative phases oi the M. F.s in the sections.

' Fig. 16 may be also regarded as representin a winding of 162 sections, each of the sections shown standing for three evenly spaced sections in series; thus, section a l would represent sections 5 1, 108, and 162 in series and 27 would represent 27, 81 and 135 in series. Such a 162 section winding will act as a primary on 18 poles and as a second ary 011 6 poles.

If starting resistances can be dispensed with, as when a large starting torque is not required, the winding may have 18 sections only, each phase still containing three parallel branches, with corresponding pairs 01 the three branches spaced equally round the machine, and each branch comprising only a single mutually reversed pair of diametrically opposite sections. One phase of a winding arranged in this way is illustrated in Fig. 17.

The conditions which any winding must fulfil which is to act simultaneously as a primary on one pole number and as a secondary capable of resistance control on another are broadly as follows:

(1) The sum of the E. M. F.s round any circuits which remain closed when the resistances are open circuited must be zero (or very small). This is to ensure that all secondary currents pass through the resistances and do not circulate within the. wind ing itself, which would make regulation impossible.

(2) The sum of the secondary currents flowing towards any junction point of sev eral parallel circuits must be zero. This is to ensure that primary and secondary currents shall be independent so that they may flow simultaneously in the same circuit.

Cascade primary win-dings usually contain a number of parallels and the simplest way to satisfy the first condition is to ensure that the sum of the secondary E. M. F.s in each parallel shall be zero. This has been done in the i-section element described with reference to Figure 1 1. In the winding of Figure 16 the same aim is attained by connecting in series three evenly spaced sections, for there will be thesame E. M. F. in all of them on 6 poles, and on 2 poles they will term a balanced three phase system. In the winding of Figure 16 instead of three simple sections, there are three units connected in series, each comprising two opposite sections, as 1 and 28. They are, it is true, not quite evenly spaced apart, and their phases will not be exactly at 120; but an approximate compliance with the condition is sultlcient. The first of the above conditions is thus met. To satisfy the second the winding is made with three parallels. corresponding sections of the three parallels being sections evenly spaced around the machine, as 18, 36, The sum of the secondary currents flowing to the junction point of the parallels 18, and 54. is zero and thus these secondary currents form a balanced polypliase system.

Even the slight departure from the theolc/ck retically desirable condition involved in connecting in series sections which are not evenly spaced may be avoided by the use of overlapping sections, several sections being wound into one slot. But this complication is not ustitied, for the inexactness will only leave an out-of-balance E. M. F. of about 6% of the E. M. F. across one branch of the winding; and this will produce a circulating current only at starting when the resistances are disconnected; which, moreover, will be small since it must pass through six sections in series; and such as it is will contribute to the starting torque. The effect of these residual currents is not serious, and may be further diminished by connecting corresponding branches only together, forming three star points instead of one, and connecting an additional rheostat to join these star points.

Figure 18 shows the windings of one form of machine according to the present invention. The machine has one winding on the rotor RW and two windings on the stator SW, SW. The winding Fill is of i8 sec tions connected in a mesh-star arrangement analogous to that oi Figure 8 with the exception that instead of the inner ring shortcircuiting halt the terminals, the ends of the star sections are brought out to terminals. The winding is thus connected to tern inals each of which is connected to an even numbered section. The pitch of each coil of a. section may vary within wide limits whereby various ratios of flux densities may be obtained and may diifer from the pitch of a winding resulting from the super-position of two component windings. These terminals are connected to switches E, F. Z Z Z show typical connections from the winding RlV to the switches E, F. To enable this winding to be used as a secondary, control apparatus must be provided for connecting certain of the terminals together directly and through resistances. F is the switch by which this arrangement brought about and are the resistances. The switch E provides means for connecting the winding to three terminals V, V, and X so that when it is delivering three phase current, such current may be passed to the stator winding. The winding RV, is adapt-ed for 6, 8, 16, i8 poles. The stator winding SW is ot the form illustrated in Fig. 14 of the drawings, that is, it consists of a winding of 2%: sections and is built up of units each of which includes 4 sections evenly spaced around the periphery of the stator and arranged to form two parallel paths each consisting of a pair of sections reversed. In each unit the j u1ictions of the two pairs of reversed sections are connected through a variable resistance It. Six such units numbered 1 to (3 by tne number of the lowest numbered section in it are joined in a three-sided mesh, cach side being formed by a pair of units in series.

The terminals 0 nected to a swit Tl e winding SW adapted a for 8 poles. The stator winding ill 1' the form illustrated in Fig. 1c and has fully described with reference to s d iigr. The terminals P, Q, R are connected to a switch B by which the winding may be connected to the supply L L ii. The wind ing Sli is adapted as a prirary for 18 poles. The terminals P, Q, R of the winch ing are also connected to a switch C. The terminals V, Fit X ot' the switch it are connected to a switch D.

For the machine to run at the 24,- pole casrade speed the switches A and F are closed whereby the winding Sli is connectec to the supply. On gradually cutting out the resistance III/ the machine will rise from standstill to the A pole speed. On cutting out the resistances Z: it will rise from the pole cascade speed to the 8 pole basal speed.

closing the switches i5 and the winding Si will be connected to the supply instead of SW and on cutting out the resistances 3 which correspond to the resistances 1 2 of Fig. 16 the machine will also rise from standstill to the 24: pole cascade'sf ed. ()n cutting out the resistances 7.1 it will rise from the 2spole speed to the 18 pole basal speed.

it the switch ll be closed the terminals of the rotor winding RlV will be connected in sets of 8 so that three phase currents may be led off from it at the terminals V, TV, X; by closing switch A, the winding Si t is connected to the supply; by closing switch C the three phase current from the rotor winding RVV will be delivered to the stator winding SVV through variable resistances 1. On. gradually cutting out the resistances 1 the machine will rise to and run at the 26 pole cascade speed and on opening the switch (7 and closing the switch D the termin s N, X are shortcircuited tl i 'h the i so ances 1., on. the cutting out of which the machine will rise to the 8 pole basal speed.

Although cascade motors may be onstructed tor any coi'nbination oi pole numbers, yet some such combinations may prove inoperative due to want of magnetic balance, the magnetic pull on the rotor not. being balanced in all directions and therefore cruising deflection of the shaft.

It was formerly thouglit that to secure magnetic balance the numbers ot pole pairs of the two component fields must have a common factor. But since magnetic pull is proportional to the square of the flux density, it is suiiicient to ensure balance it. any value of the square of the this: density which occurs at one point occurs also at one or more other points evenly spaced around the rotor with respect to the first. This condition is fulfilled not only when the two numbers of pole pairs have a common factor, but also when they are prime to one another and. both odd. For in any field of an odd number of pole pairs diametrically opposite points have equal and opposite magnetic densities; so that the resultant of two such fields must also present equal and opposite densities at diametrically opposite points.

Since the secondary winding not joined to any external circuit the induced on :ents must flow in closed circuits in the winding, and since they are balanced polyphase currents there must be a multiplicity ot such circuits, equally spaced around the circumference of the secondary member. in OM01 that cascade action may occur the E. M. F.

induced in the secondary winding by the primary field must excite a secondary field of a different number of poles, and the E. M. i due to this secondary field cutting the secondary winding must balance that due to the primary field in all the closed circuits of the winding. This involves that the two E. M. F.s generated by the two fields considered separately must be of the same trequency and oi equal magnitude and opposite phase in each such circuit and not in one only.

This condition establishes the relation between the number of phases in the secondary winding, (and hence the number of sections) and the ratio of the two pole numbers of the machine. It the two numbers of pole pairs P and Q have a common factor CF, the circumference of the machine will present CF similar Zones, the quantities P and are the numbers of pole pairs in one 01" these CF identical zones, i. e., the numbers of pole pairs divided by their G. C. M. It, then two fields of P and Q pole pairs respectively are to produce E. M. F35; of opposite phase in each of n equally spaced sections, the phase difference between the l l. M. Fla induced in neighbouring sections by the one field must be equal to the pl Cllll iGI'CDCO between the E- M. lTs induced in the said neighbouring sections by the other field. From this it is deduced that ii the two fields rotate in opposite directions-the number of sections a must be equal to or a multiple of P +Q and E. M. 753s oi? i -P11 phases must be generated in them.

That the E. M. F.s generated by the two fields will. be oi? the same frequency follows from the fact that the .L22'1&i111'8 rotates at cascade speed. The provision that they shall be or" equal magnitude and opposite phase determines the magnitude and phase ot the secondary flux.

In an ideal internal cascade machine there would be two harmonic space distributions of ampere-conductors of different pole numbers rotating uniformly, say in opposite directions, at speeds inversely proportional to the pole numbers. A study of the distribu tion of ampere conductors corresponding to the resultant of two such component distributions will show what is to be aimed at in the design of a winding, which, being concentrated at particular points of the circumi erence, namely the rotor slots can only approximate to the ideal distribution.

Referring to Fig. 1 the ampere-conductors per unit length at any point 1 oil the circumference may be represented in wellknown manner by the project-ion upon a datum line C Z of a vector C supposed to rotate uniformly at a speed corresponding to t e frequency. C is the position of the vector at a particular instant herein called the initial instant. The ampere-conductors at any other point or" the circumference corresponding to this same component distribu tion can be represented by a vector of the same length rotating at the same speed, and only differing from C in its position at the initial instant. Let the c' 'cumterencc be divided into any arbitrary number of parts, say 36. If the field is a Q-pcle field, the vector corresponding to the point 2 would pass through 2 at the initial instant, and so on; that is to say, the vector corresponding to any second point would differ from the vector corresponding to the starting point 1 by the same angle as separates the second pointfrom the starting point. In Figure 1. it is supposed that the first component field is a l-pole field. Therefore the ampere-conductors at point 19, must be of: the same phase as at the d ametrically opposite point 1, i. e. are represented by the same vector C or C and the ampere-conductors at the point 10 will be of opposite phase, and are represented by the vector C passing through the point 19. For the l-pole field then, the vector for any second point difiers from the vector {or the starting point by twice the angle separating the second point from the starting point. And generally for a field 0t P pole p second point will di from the vector f .1- times the angle the starting point by L which separates the second point from ti 2 starting point.

ln Fig. l, the vectors corresponding to particular points of the circumference are distinguished by appropriate lettering. The points on the inner circle representing the circumference are numbered consecutively l to 36; the points on the next circle, as 1% 2% representing the vectors corresponding to a l-pole field have twice the angular spacing ot those on the first, and are also numbered consecutively, with the result that each bears two numbers.

The second component field chosen for illustration in Figure 1 is 6-pole field rotating in the opposite direction to the 4- pole field. The points on the outer circle a rs the vector for any have therefore three times the angular displacement oi those on the inner circle, and are numbered consecutively in the opposite direction; each bears three numbers, as 4;, 16 28*.

A vector regrcsenting the ampere-conductors for any point of the circumference corresponding to the resultant field may be obtained by compounding the component vectors for that point. The two vectors C and C are shown thus compounded, giving the vector C. If a sutlicient number of such resultant vectors be plotted the curve shown in F 1 is obtained. Any line drawn from C to this curve, as 0*, is a vector which, it rotating uniformly at a speed corresponding to the frequency, represents by its projection on the datum line C Z the ampere-conductors at a corresponding point, as 2, on the circumference of the rotor.

This is a five-lobed curve, with five maxima equal tot-he sum of the radii C d-C and live minima equal to their difference. The number of maxima is determined by the ratio of the two numbers of poles. For a maximum occurs each time the vectors for the two component fields coincide. It the fields are or" P and Q} pole pairs respectively and move in opposite directions, then while the vector for field P moves through an angle X that for field Q moves through an angle Starting from a point on the rotor, as 1, for which the vectors coincide, they will coincide again when the sum of the angles through which they have moved is equal to 360, i. e. when i. 0., when the vector for the field P has moved through an angle and that for field Q through an angle T Q 360 P ta" They might equally well represent the E. M. Fs per bar or section due t'o two oppositely revolvin fields; when the same argument would show that there are only P Q} positions where there is a coincidcnce of phase of the l l. M. FPS due to two such fields, or where there is exact opposition of phase it one field be reversed in phase. Hence it only at P +Q points that the two E. cancel by a right adjustment of their mag nit-tides. It follows that, as above stated, (save for the exceptional cases where several points of phase opposition can be included in one circuit), secondary windings for P and Q pole pairs must have P i-Q} equally spaced circuits.

For fields rotating in the same direction,

the number of maxima in the distribution the distribution curve are fixed relatively to the windii'ig to which the distribution is due and are equidistant in space and phase. All the lobes of the curve are of the same shape, and differ only in phase. Hence a winding to give rise to such a curve of dis tributien must have in it at least as many phases as those of the maxima P i-Q (or. twice as many if conductors carrying op positecurrents are counted as of opposite phases). It is sometimes found however that a gr iter number of phases enables the distribution curve to beimore exactly produced; and since an extra phase or phases added to the part of the winding producing one lobe involves corresponding additions to all other parts, the total number of phases may require to be some multiple c The relation of the phases .to one another must be invariable, so, that the number of phases can only be thus mul tiplied, if the multiplication can be brought about by the inter-connection of the sections of the winding in star and mesh, for example as described above with reference to Fig. 2. The winding of Fig. 2 produces only five maxima, and the corresponding diagram (Fig. 8) shows only five circuits, yet owing to the star mesh connection there are 10 phases present (or 20 if conductors carrying opposite currents are counted as opposite phases).

It may now be seen that a winding capable of having 5-phase currents generated in it,

and characterized by five maxima in the.

curve of distribution of its anupere-conductors is required not only for fields of 1 and 4-. pole pairs, and 2 and 3 pole pairs rotating in opposite directions, but also for fields of 1 and 6 pole pairs, ant. so on, rotating in the same direction; and a 'Z-phase winding with 7 maxim-a is similarly appropriate to 5 and 2 pole pairs, and so on. Fi l-iether a M. Fs can be made to bid densities of the component fields 12 being about the same for both pairs of pole numbers.

The flux density for a winding or" given pitch may be calculated on well known principles; convenient formulae for the types of winding chiefly in question in this specification will be found in a paper read by the applicant before the British Institution of Electrical Engineers on April 12th 1921.

The curve of distribution shows the essential characteristic of the winding to be a definite number 7Z:P1+Q,1 of points of maxin'ium ampere-conductors. A simple type of winding which possesses this characteristic is a single-phase winding for n P -l-Q poles. Such a winding consists of '21 bands of ampereconductors alternately opposite in phase (forming a maxima), and as a rule it spaces intermediate between the bands in which the slots are unwound, forming 91- ininima. In such a single phase winding one end of each of the a hands may be joined to a common point, while of the remaining ends the odd ones may all be con- 7 nected to one terminal and the even to another.

.A single phase winding so connected may be regarded as a rudimentary type of cascade winding; for it the two single-phase terminals are short-circuited each of the n poles is independently short-circuited and therefore a balanced system of a phase currents can circulate in them as was previously seen to be necessary for a cascade winding on P and Q} pole pairs. Such a single phase winding may therefore be taken as the basis for constructing a winding which will give more exactly the desired distribution. The winding may be either concentric or of the drum type.

Vfindings consisting of two superposed windings in which portions may be cancelled or substituted by others may be selected, and the extent of possible cancellation determined, from the considerations next set forth. There the resultant winding is of the drum type it is to be noted that the pitch is one of the variables at the disposal of the designer; it will partly be determined by calculations similar to those for determining the ratio of the densities of the primary and secondary fluxes, and partly by reference to the ideal curve of distribution. Vvindings are known which have been derived by supcrposing two component windings, one for each pole number, cancelling those bars which lie in the same slots and carry equal and opposite currents; compounding bars carrying currents of a certain phase dili'erence and reconnecting the bars of the winding. W indings produced in this manner are completely determined in every respect so that their pitch cannot be varied. The windings according to the present in vention are not subject to this limitation and may be produced with widely varying pitches.

It has been pointed out that for winding to operate on P and Q} pole pairs, it must be capable of carrying currents in '7L:P l- Q phases, and must therefore be divided into at least 42 sections. In n such sections (or any sub-multiple of a) the order of the phases in a field of P pole pairs revolving clockwise is the same as in a field of Q} pole pairs revolving counter-clockwise. But the winding may contain any multiple of a, say 1%, sections; it may then be treated as r groups of 07. sections each. Number these groups in clockwise order 1 to r. Then 1":11 or if r and n have no common factor, changing from P pole pairs rotating one way to Q pole pairs rotating the other way will change the phase of the s group by If n and T have a common factor F) so that n bm and rzb, a similar rule applies if the winding be considered as resolved into In groups of only m sections each, at being thus a sub-multiple of P +Q This rule shows how many sections of two such winding will cancel on superposition. For it 1 :2, then for the second groups (8 2),

If, therefore, two windings of '2'- 01 sections, one having the requisite phases for P pole pairs and the other those for Q pole pairs rotating in opposite directions, are superposed, the second groups of the two windings will cancel; that is, half the sections cancel on superposition; and "for l e superposed sections that do not cancel a single section of intermediate phase can be substituted.

Vhether the, winding resulting from this superposition cancellation and substitution will give good results can be ascertained by drawing the distribution curve in the manner already described. It will sometimes happen that a better approximation to the ideal curve will be given by windings in which not so many as halt the sections are cancelled. If r d,

when 3:3, but not when 5:1, 2 or 4t; hence in this case one quarter of the sections would cancel. Thus it windings for P Q} pole pairs respectively are both made up of 1' llU 1,5ea47e (P +Q sections, they can be superposed l in such a manner that ;th of the sections will be eliminated. The ampere-conductor distribution of a winding compounded in this way can be compared with the ideal curve of ampere-conductors; and slight modifications of the winding, for instance, of its pitch, the effect of which is tested in the manner described above, may be made so as to cause it to yield a curve as close as possible to the ideal.

Finally, curves similar to those of Fig. 1 may be drawn for the windings described with reference to Figs. 2 and 8.

Now the resultant of two unit currents differing in phase by 0 degrees is 2 sin (1SO-0). Hence the current in any star-connected bar, (for instance the upper conductor of slot 5) is equal to 2 sin (l80-36) times the current in a meshconnected bar (for instance the lower conductors of slots 7 and 9, i. e. star current:2 sin 72 (mesh current) :1..9 (mesh current).

The distribution of ampere-conductors may be examined by means of a diagram like that of Fig. 1. As shown in Fig. 5 draw first two circles of radii in the ratio of 1:1.9; i. e. proportional to the mesh and star currents respectively. Mark on them each of the phase angles that occur in the winding in mesh and star bars respectively; for instance theangles 0, 180, 1 H", 324 on the inner circle corresponding with the mesh bars in slots &, 7, 9, 6; and 3&2 and 162 on the outer circle corresponding with the star bars in slots 5 and 8. At each point thus marked show the numbers of the slots containing bars of that phase, the mesh bars on the inner circle and the star bars on the outer. Then compound all the vectors as 5, 5*, which bear the number of any particular slot, as is shown for slot 5, obtaining the resultant ampereconductors of the slot whit-hare indicated bya Roman figure, as 7. By joining the ends of these resultants a polygonal distribution diagram (in dotted lines) is obtained showing five lobes, and quite closely approinmating to the ideal distribution curve.

I 3 shows the phases of the conductors for 2 and 8 poles when the phase difference between the circuits is 72 or 288 respectively. Fig. 6 shows the distribution of ampere-conductors, obtained in the way just described for Fig. 5, but with circles of radii in the ratio of 1.17 :1 which is the ratio of the star to the mesh currents for this case.

What I claim is 1. An internal cascade machine comprising a stator and a rotor, polyphase windings on said members which produce fields of difi'ercnt numbers of pole pairs the sum Or difference of which, divided by their G. C. M. is greater than three, the winding on one member producing a number of equally spaced maxima of ampere conductors equal to the algebraic difference oi the nun'ibers of pole pairs in the two fields (taking account of the relative directions of rotation of the two fields).

2. An internal cascade machine comprising a stator and a rotor, polyphase windings on said members which produce fields o'i difi'crent numbers of pole pairs the sum or difi'erence oi? which, divided by their G. ti. M. is greater than three, the winding on one member producing a number of equally spaced maxim-a oi ampere conductors equal to the algebraic difference of the numbers of pole pairs in the two fields (taking account of the relative direction of rotation of the two fields), and the number of active conductors per slot having a corresponding number of maxima.

3. An internal cascade machine comprising a stator and a rotor, polyphase windings on said members which produce fields of dii'ierent numbers of pole pairs the sum or difference oi which, divided by their (at. C. M. is greater than three, the winding on one member producing a number of equally spaced maxima of ampere conductors equal to the algebraic difference of the numbers of pole pairs in the two'fields (taking account of the relative directions of rotation of the two fields) and comprising sections connected into a mesh of more than three sides carrying currents of different phases, each side containing two mutually opposed sections connected in series and other sections forming an equal number of star arms, one connected to each angle of the mesh.

4;. An internal cascade machine comprising a stator and a rotor, polyphase windings on said members which produce fields of different numbers of pole pairs the sum of difference of which, divided by their G. C. M. is greater than three, the winding on one member producing a number of equally spaced maxima of ampere conductors equal to the algebraic difi'erence or" the numbers of pole pairs in the two fields (taking account of the relative direction of rotation of the two fields), and the number of active conductors per slot having a corresponding number of maxima and comprising sections connected into a mesh of more than three sides carrying currents of ditlerent phases, each side containing two mutually opposed sections connected in series and other seotions forming an equal number or" star arms, 

